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An excellent but by now slightly outdated reference for all kinds of core equivalence theorems is Hildenbrand's book "Core and Equilibria of a Large Economy". You can probably get references on more recent literature in the Aliprantis, [View full text and thread]

I don't know of work by K. Arrow on core equivalence. See Debreu and Scarf, International Economic Review, 1963; Anderson, Econometrica, 1978 and for a nice discussion on this topic see B. Ellickson, Competitive Equilibrium, [View full text and thread]